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Some define statistics as the field that focuses on turning information into knowledge. The first step in that process is to summarize and describe the raw information - the data. In this lab we explore flights, specifically a random sample of domestic flights that departed from the three major New York City airport in 2013. We will generate simple graphical and numerical summaries of data on these flights and explore delay times. As this is a large data set, along the way you’ll also learn the indispensable skills of data processing and subsetting.
In this lab we will explore the data using the dplyr package and visualize it using the ggplot2 package for data visualization. The data can be found in the companion package for this course, statsr.
Let’s load the packages.
library(statsr)
library(dplyr)
library(ggplot2)The Bureau of Transportation Statistics (BTS) is a statistical agency that is a part of the Research and Innovative Technology Administration (RITA). As its name implies, BTS collects and makes available transportation data, such as the flights data we will be working with in this lab.
We begin by loading the nycflights data frame. Type the following in your console to load the data:
data(nycflights)The data frame containing 32735 flights that shows up in your workspace is a data matrix, with each row representing an observation and each column representing a variable. R calls this data format a data frame, which is a term that will be used throughout the labs.
To view the names of the variables, type the command
names(nycflights)## [1] "year" "month" "day" "dep_time" "dep_delay"
## [6] "arr_time" "arr_delay" "carrier" "tailnum" "flight"
## [11] "origin" "dest" "air_time" "distance" "hour"
## [16] "minute"
This returns the names of the variables in this data frame. The codebook (description of the variables) is included below. This information can also be found in the help file for the data frame which can be accessed by typing ?nycflights in the console.
year, month, day: Date of departuredep_time, arr_time: Departure and arrival times, local timezone.dep_delay, arr_delay: Departure and arrival delays, in minutes. Negative times represent early departures/arrivals.carrier: Two letter carrier abbreviation.
9E: Endeavor Air Inc.AA: American Airlines Inc.AS: Alaska Airlines Inc.B6: JetBlue AirwaysDL: Delta Air Lines Inc.EV: ExpressJet Airlines Inc.F9: Frontier Airlines Inc.FL: AirTran Airways CorporationHA: Hawaiian Airlines Inc.MQ: Envoy AirOO: SkyWest Airlines Inc.UA: United Air Lines Inc.US: US Airways Inc.VX: Virgin AmericaWN: Southwest Airlines Co.YV: Mesa Airlines Inc.tailnum: Plane tail numberflight: Flight numberorigin, dest: Airport codes for origin and destination. (Google can help you with what code stands for which airport.)air_time: Amount of time spent in the air, in minutes.distance: Distance flown, in miles.hour, minute: Time of departure broken in to hour and minutes.A very useful function for taking a quick peek at your data frame, and viewing its dimensions and data types is str, which stands for structure.
str(nycflights)## Classes 'tbl_df' and 'data.frame': 32735 obs. of 16 variables:
## $ year : int 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 ...
## $ month : int 6 5 12 5 7 1 12 8 9 4 ...
## $ day : int 30 7 8 14 21 1 9 13 26 30 ...
## $ dep_time : int 940 1657 859 1841 1102 1817 1259 1920 725 1323 ...
## $ dep_delay: num 15 -3 -1 -4 -3 -3 14 85 -10 62 ...
## $ arr_time : int 1216 2104 1238 2122 1230 2008 1617 2032 1027 1549 ...
## $ arr_delay: num -4 10 11 -34 -8 3 22 71 -8 60 ...
## $ carrier : chr "VX" "DL" "DL" "DL" ...
## $ tailnum : chr "N626VA" "N3760C" "N712TW" "N914DL" ...
## $ flight : int 407 329 422 2391 3652 353 1428 1407 2279 4162 ...
## $ origin : chr "JFK" "JFK" "JFK" "JFK" ...
## $ dest : chr "LAX" "SJU" "LAX" "TPA" ...
## $ air_time : num 313 216 376 135 50 138 240 48 148 110 ...
## $ distance : num 2475 1598 2475 1005 296 ...
## $ hour : num 9 16 8 18 11 18 12 19 7 13 ...
## $ minute : num 40 57 59 41 2 17 59 20 25 23 ...
The nycflights data frame is a massive trove of information. Let’s think about some questions we might want to answer with these data:
The dplyr package offers seven verbs (functions) for basic data manipulation:
filter()arrange()select()distinct()mutate()summarise()sample_n()We will use some of these functions in this lab, and learn about others in a future lab.
We can examine the distribution of departure delays of all flights with a histogram.
ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
This function says to plot the dep_delay variable from the nycflights data frame on the x-axis. It also defines a geom (short for geometric object), which describes the type of plot you will produce.
Histograms are generally a very good way to see the shape of a single distribution, but that shape can change depending on how the data is split between the different bins. You can easily define the binwidth you want to use:
ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 15)ggplot(data = nycflights, aes(x = dep_delay)) +
geom_histogram(binwidth = 150)How do these three histograms with the various binwidths compare?
If we want to focus on departure delays of flights headed to RDU only, we need to first filter the data for flights headed to RDU (dest == "RDU") and then make a histogram of only departure delays of only those flights.
rdu_flights <- nycflights %>%
filter(dest == "RDU")
ggplot(data = rdu_flights, aes(x = dep_delay)) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Let’s decipher these three lines of code:
nycflights data frame, filter for flights headed to RDU, and save the result as a new data frame called rdu_flights.
== means “if it’s equal to”.RDU is in quotation marks since it is a character string.ggplot call from earlier for making a histogram, except that it uses the data frame for flights headed to RDU instead of all flights.Logical operators: Filtering for certain observations (e.g. flights from a particular airport) is often of interest in data frames where we might want to examine observations with certain characteristics separately from the rest of the data. To do so we use the filter function and a series of logical operators. The most commonly used logical operators for data analysis are as follows:
== means “equal to”!= means “not equal to”> or < means “greater than” or “less than”>= or <= means “greater than or equal to” or “less than or equal to”We can also obtain numerical summaries for these flights:
rdu_flights %>%
summarise(mean_dd = mean(dep_delay), sd_dd = sd(dep_delay), n = n())## # A tibble: 1 x 3
## mean_dd sd_dd n
## <dbl> <dbl> <int>
## 1 11.7 35.6 801
Note that in the summarise function we created a list of two elements. The names of these elements are user defined, like mean_dd, sd_dd, n, and you could customize these names as you like (just don’t use spaces in your names). Calculating these summary statistics also require that you know the function calls. Note that n() reports the sample size.
Summary statistics: Some useful function calls for summary statistics for a single numerical variable are as follows:
meanmediansdvarIQRrangeminmaxWe can also filter based on multiple criteria. Suppose we are interested in flights headed to San Francisco (SFO) in February:
sfo_feb_flights <- nycflights %>%
filter(dest == "SFO", month == 2)Note that we can separate the conditions using commas if we want flights that are both headed to SFO and in February. If we are interested in either flights headed to SFO or in February we can use the | instead of the comma.
Create a new data frame that includes flights headed to SFO in February, and save this data frame as sfo_feb_flights. How many flights meet these criteria?
# type your code for Question 1 here, and Knit
nrow(sfo_feb_flights)## [1] 68
Make a histogram and calculate appropriate summary statistics for arrival delays of sfo_feb_flights. Which of the following is false?
# type your code for Question 2 here, and Knit
ggplot(data = sfo_feb_flights, aes(x = arr_delay)) + geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Another useful functionality is being able to quickly calculate summary statistics for various groups in your data frame. For example, we can modify the above command using the group_by function to get the same summary stats for each origin airport:
rdu_flights %>%
group_by(origin) %>%
summarise(mean_dd = mean(dep_delay), sd_dd = sd(dep_delay), n = n())## # A tibble: 3 x 4
## origin mean_dd sd_dd n
## <chr> <dbl> <dbl> <int>
## 1 EWR 13.4 32.1 145
## 2 JFK 15.4 40.3 300
## 3 LGA 7.90 32.2 356
Here, we first grouped the data by origin, and then calculated the summary statistics.
Calculate the median and interquartile range for arr_delays of flights in the sfo_feb_flights data frame, grouped by carrier. Which carrier has the highest IQR of arrival delays?
# type your code for Question 3 here, and Knit
sfo_feb_flights %>%
summarise(mean_ad = mean(arr_delay), sd_ad = sd(arr_delay),
n = n(), max_ad = max(arr_delay), min_ad = min(arr_delay))## # A tibble: 1 x 5
## mean_ad sd_ad n max_ad min_ad
## <dbl> <dbl> <int> <dbl> <dbl>
## 1 -4.5 36.3 68 196 -66
Which month would you expect to have the highest average delay departing from an NYC airport?
Let’s think about how we would answer this question:
group_by months, thensummarise mean departure delays.arrange these average delays in descending ordernycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay)) %>%
arrange(desc(mean_dd))## # A tibble: 12 x 2
## month mean_dd
## <int> <dbl>
## 1 7 20.8
## 2 6 20.4
## 3 12 17.4
## 4 4 14.6
## 5 3 13.5
## 6 5 13.3
## 7 8 12.6
## 8 2 10.7
## 9 1 10.2
## 10 9 6.87
## 11 11 6.10
## 12 10 5.88
Which month has the highest average departure delay from an NYC airport?
# type your code for Question 4 here, and Knit
nycflights %>%
group_by(month) %>%
summarise(mean_dd = mean(dep_delay)) %>%
arrange(desc(mean_dd))## # A tibble: 12 x 2
## month mean_dd
## <int> <dbl>
## 1 7 20.8
## 2 6 20.4
## 3 12 17.4
## 4 4 14.6
## 5 3 13.5
## 6 5 13.3
## 7 8 12.6
## 8 2 10.7
## 9 1 10.2
## 10 9 6.87
## 11 11 6.10
## 12 10 5.88
Which month has the highest median departure delay from an NYC airport?
# type your code for Question 5 here, and Knit
nycflights %>%
group_by(month) %>%
summarise(median_dd = median(dep_delay)) %>%
arrange(desc(median_dd))## # A tibble: 12 x 2
## month median_dd
## <int> <dbl>
## 1 12 1
## 2 6 0
## 3 7 0
## 4 3 -1
## 5 5 -1
## 6 8 -1
## 7 1 -2
## 8 2 -2
## 9 4 -2
## 10 11 -2
## 11 9 -3
## 12 10 -3
Is the mean or the median a more reliable measure for deciding which month(s) to avoid flying if you really dislike delayed flights, and why?
We can also visualize the distributions of departure delays across months using side-by-side box plots:
ggplot(nycflights, aes(x = factor(month), y = dep_delay)) +
geom_boxplot()There is some new syntax here: We want departure delays on the y-axis and the months on the x-axis to produce side-by-side box plots. Side-by-side box plots require a categorical variable on the x-axis, however in the data frame month is stored as a numerical variable (numbers 1 - 12). Therefore we can force R to treat this variable as categorical, what R calls a factor, variable with factor(month).
Suppose you will be flying out of NYC and want to know which of the three major NYC airports has the best on time departure rate of departing flights. Suppose also that for you a flight that is delayed for less than 5 minutes is basically “on time”. You consider any flight delayed for 5 minutes of more to be “delayed”.
In order to determine which airport has the best on time departure rate, we need to
Let’s start with classifying each flight as “on time” or “delayed” by creating a new variable with the mutate function.
nycflights <- nycflights %>%
mutate(dep_type = ifelse(dep_delay < 5, "on time", "delayed"))The first argument in the mutate function is the name of the new variable we want to create, in this case dep_type. Then if dep_delay < 5 we classify the flight as "on time" and "delayed" if not, i.e. if the flight is delayed for 5 or more minutes.
Note that we are also overwriting the nycflights data frame with the new version of this data frame that includes the new dep_type variable.
We can handle all the remaining steps in one code chunk:
nycflights %>%
group_by(origin) %>%
summarise(ot_dep_rate = sum(dep_type == "on time") / n()) %>%
arrange(desc(ot_dep_rate))## # A tibble: 3 x 2
## origin ot_dep_rate
## <chr> <dbl>
## 1 LGA 0.728
## 2 JFK 0.694
## 3 EWR 0.637
If you were selecting an airport simply based on on time departure percentage, which NYC airport would you choose to fly out of?
# type your code for Question 7 here, and Knit
nycflights %>%
group_by(origin) %>%
summarise(ot_dep_rate = sum(dep_type == "on time") / n()) %>%
arrange(desc(ot_dep_rate))## # A tibble: 3 x 2
## origin ot_dep_rate
## <chr> <dbl>
## 1 LGA 0.728
## 2 JFK 0.694
## 3 EWR 0.637
We can also visualize the distribution of on on time departure rate across the three airports using a segmented bar plot.
ggplot(data = nycflights, aes(x = origin, fill = dep_type)) +
geom_bar()Mutate the data frame so that it includes a new variable that contains the average speed, avg_speed traveled by the plane for each flight (in mph). What is the tail number of the plane with the fastest avg_speed? Hint: Average speed can be calculated as distance divided by number of hours of travel, and note that air_time is given in minutes. If you just want to show the avg_speed and tailnum and none of the other variables, use the select function at the end of your pipe to select just these two variables with select(avg_speed, tailnum). You can Google this tail number to find out more about the aircraft.
# type your code for Question 8 here, and Knit
nycflights <- nycflights %>%
mutate(avg_speed = (distance*60)/air_time)
nycflights %>%
select(avg_speed, tailnum) %>%
arrange(desc(avg_speed))## avg_speed tailnum
## 1 703.3846 N666DN
## 2 557.4419 N779JB
## 3 554.2197 N571JB
## 4 547.8857 N568JB
## 5 547.8857 N5EHAA
## 6 547.8857 N656JB
## 7 544.7727 N789JB
## 8 538.6517 N516JB
## 9 535.6425 N648JB
## 10 535.6425 N510JB
## 11 533.0387 N38268
## 12 533.0387 N53442
## 13 533.0387 N75858
## 14 532.6667 N624JB
## 15 532.6667 N569JB
## 16 532.6667 N3749D
## 17 531.2360 N523JB
## 18 529.7238 N504JB
## 19 529.7238 N637JB
## 20 529.7238 N506JB
## 21 529.1209 N571UA
## 22 527.2131 N37267
## 23 526.8132 N608JB
## 24 526.8132 N3771K
## 25 526.8132 N595JB
## 26 526.3784 N5ETAA
## 27 526.1131 N76065
## 28 525.4144 N26208
## 29 525.4144 N37419
## 30 524.5082 N439UA
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## 8454 437.7273 N404UA
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## 8465 437.6712 N830UA
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## 8471 437.6712 N73283
## 8472 437.6712 N77296
## 8473 437.6712 N663JB
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## 8476 437.6712 N535JB
## 8477 437.6250 N842UA
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## 8480 437.5000 N11206
## 8481 437.5000 N67058
## 8482 437.5000 N14731
## 8483 437.5000 N57439
## 8484 437.5000 N16732
## 8485 437.5000 N815UA
## 8486 437.5000 N672UA
## 8487 437.4888 N506JB
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## 8490 437.4684 N851UA
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## 8492 437.4468 N554JB
## 8493 437.4468 N589JB
## 8494 437.4468 N760JB
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## 8496 437.4468 N709JB
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## 8498 437.3626 N510JB
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## 8500 437.3626 N3758Y
## 8501 437.3626 N646JB
## 8502 437.3626 N523JB
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## 8507 437.3239 N397DA
## 8508 437.3239 N655JB
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## 8513 437.2159 N621VA
## 8514 437.2159 N77258
## 8515 437.2159 N522UA
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## 8520 437.2159 N33132
## 8521 437.2159 N37465
## 8522 437.2159 N802UA
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## 8528 437.1429 N535MQ
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## 8532 437.1429 N359NW
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## 8535 437.1429 N518MQ
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## 8538 437.1429 N534MQ
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## 8541 437.0704 N532UA
## 8542 437.0704 N711ZX
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## 8550 437.0704 N846VA
## 8551 437.0704 N324AA
## 8552 437.0704 N505UA
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## 8558 437.0455 N717EV
## 8559 437.0455 N760EV
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## 8564 436.9620 N13718
## 8565 436.9565 N709JB
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## 8569 436.9565 N552JB
## 8570 436.9565 N804JB
## 8571 436.9565 N318JB
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## 8573 436.9565 N634JB
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## 8575 436.9565 N504MQ
## 8576 436.9565 N501MQ
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## 8578 436.9565 N589JB
## 8579 436.9565 N648JB
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## 8593 436.9128 N3GXAA
## 8594 436.9128 N5EDAA
## 8595 436.9128 N34460
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## 8618 436.7890 N332NW
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## 8620 436.7857 N3HWAA
## 8621 436.7857 N536JB
## 8622 436.7857 N591JB
## 8623 436.7857 N563JB
## 8624 436.7857 N661JB
## 8625 436.7832 N279JB
## 8626 436.7832 N612JB
## 8627 436.7647 N154DL
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## 8634 436.7647 N329AA
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## 8644 436.7647 N709TW
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## 8646 436.7647 N784JB
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## 8650 436.7273 N38451
## 8651 436.7213 N777QC
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## 8658 436.6667 N21108
## 8659 436.6667 N611QX
## 8660 436.6572 N590JB
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## 8662 436.6507 N612JB
## 8663 436.6507 N3GGAA
## 8664 436.6507 N729JB
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## 8666 436.6423 N87527
## 8667 436.6423 N37434
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## 8674 436.6154 N13979
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## 8676 436.6154 N12552
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## 8679 436.5714 N716EV
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## 8683 436.5714 N501MQ
## 8684 436.5714 N515MQ
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## 8686 436.5714 N419WN
## 8687 436.5049 N640JB
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## 8690 436.5049 N746JB
## 8691 436.5049 N661JB
## 8692 436.5049 N5DUAA
## 8693 436.5049 N3HEAA
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## 8696 436.5049 N706JB
## 8697 436.5049 N3FWAA
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## 8699 436.5049 N784JB
## 8700 436.4189 N804JB
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## 8705 436.4189 N661AW
## 8706 436.3964 N3752
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## 8721 436.3351 N3CFAA
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## 8723 436.3351 N3EGAA
## 8724 436.3265 N746JB
## 8725 436.3265 N519JB
## 8726 436.3265 N3731T
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## 8730 436.3265 N709JB
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## 8732 436.3265 N629JB
## 8733 436.3265 N547JB
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## 8735 436.3265 N509JB
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## 8739 436.2500 N639JB
## 8740 436.2500 N729JB
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## 8814 435.8427 N768JB
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## 8855 435.8140 N658JB
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## 8860 435.8140 N33294
## 8861 435.7895 N238JB
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## 8875 435.7576 N519MQ
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## 8886 435.7282 N11189
## 8887 435.7282 N13913
## 8888 435.7282 N27962
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## 8891 435.6923 N27239
## 8892 435.6923 N570JB
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## 8894 435.6923 N27724
## 8895 435.6923 N565JB
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## 8898 435.6923 N531JB
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## 8900 435.6923 N16709
## 8901 435.6923 N3748Y
## 8902 435.6923 N977DL
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## 8905 435.6923 N406UA
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## 8911 435.6923 N5FAAA
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## 8913 435.6923 N503JB
## 8914 435.6923 N721TW
## 8915 435.6923 N580JB
## 8916 435.6923 N424UA
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## 8918 435.6923 N624JB
## 8919 435.6923 N708JB
## 8920 435.6923 N593JB
## 8921 435.6287 N822UA
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## 8923 435.6213 N524VA
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## 8944 435.5696 N722MQ
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## 8979 435.4967 N996DL
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## 8981 435.4896 N763JB
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## 8983 435.4896 N634JB
## 8984 435.4839 N636VA
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## 8986 435.4839 N554UA
## 8987 435.4839 N794JB
## 8988 435.4839 N853VA
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## 8994 435.4839 N1200K
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## 9008 435.4601 N369NB
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## 9010 435.4545 N539MQ
## 9011 435.4545 N504MQ
## 9012 435.4455 N514AA
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## 9058 435.4286 N508MQ
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## 9060 435.4286 N928AT
## 9061 435.4237 N521JB
## 9062 435.4237 N615JB
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## 9064 435.4079 N433AS
## 9065 435.4079 N536AS
## 9066 435.4079 N27239
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## 9068 435.4054 N558JB
## 9069 435.4054 N636JB
## 9070 435.4054 N624JB
## 9071 435.4054 N624JB
## 9072 435.4054 N630JB
## 9073 435.3982 N15986
## 9074 435.3982 N11192
## 9075 435.3982 N21154
## 9076 435.3982 N18120
## 9077 435.3982 N13994
## 9078 435.3191 N68805
## 9079 435.3191 N643JB
## 9080 435.3191 N823UA
## 9081 435.3191 N706JB
## 9082 435.3191 N87527
## 9083 435.3191 N36472
## 9084 435.3191 N39297
## 9085 435.3191 N73299
## 9086 435.3191 N68801
## 9087 435.3191 N715JB
## 9088 435.3191 N39450
## 9089 435.3191 N653JB
## 9090 435.3191 N33266
## 9091 435.3061 N200WN
## 9092 435.3061 N958WN
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## 9094 435.3061 N775SW
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## 9113 435.2332 N39728
## 9114 435.2332 N14731
## 9115 435.2000 N127UW
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## 9118 435.2000 N709EV
## 9119 435.2000 N508MQ
## 9120 435.2000 N519MQ
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Make a scatterplot of avg_speed vs. distance. Which of the following is true about the relationship between average speed and distance.
# type your code for Question 9 here, and Knit
plot(avg_speed ~ distance, data=nycflights)arr_type with levels "on time" and "delayed" based on this definition. Also mutate to create a new variable called dep_type with levels "on time" and "delayed" depending on the flight was delayed for fewer than 5 minutes or 5 minutes or more, respectively. In other words, if arr_delay is 0 minutes or fewer, arr_type is "on time". If dep_delay is less than 5 minutes, dep_type is "on time". Then, determine the on time arrival percentage based on whether the flight departed on time or not. What percent of flights that were "delayed" departing arrive "on time"?
# type your code for Question 10 here, and Knit
nycflights <- nycflights %>%
mutate(arr_type = ifelse(arr_delay <= 0, "on time", "delayed"))
nycflights %>%
group_by(dep_type) %>%
summarise(ot_arr_rate = sum(arr_type == "on time") / n()) %>%
arrange(desc(ot_arr_rate))## # A tibble: 2 x 2
## dep_type ot_arr_rate
## <chr> <dbl>
## 1 on time 0.776
## 2 delayed 0.183